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In order to know in depth the meaning of the term tessellation, it is necessary, first, to discover its etymological origin. In this case, it comes from the Latin "tesella", which can be translated as "tile", and this in turn from the Greek word "tessares", which is synonymous with "four."

The concept of tessellation not part of dictionary of the Royal Spanish Academy (RAE ). The term that does appear is tessellated , referring to what is composed of tiles . The tiles , in turn, are the different fragments that are part of a mosaic (work that is made up of different pieces or pieces).

Tessellation is called, in this way, the Pattern which follows cover a surface . Tessellation requires avoiding overlapping figures and ensuring that no blanks are registered in the coating.

For the development of the tessellation, it is usual to make reproductions of one or more tiles to cover the entire surface . It is important to note that irregular, semi-regular or regular tessellations can be performed.

The irregular tessellations they consist of polygons They are not regular. The semi-regular tessellations , meanwhile, have at least two regular polygons, while the regular tessellations they develop with regular hexagons, squares or equilateral triangles (using a single type).

In addition to these three types of exposed tessellations, the existence of a fourth type must also be noted. We are referring to the tessellations called demirregular. Under this denomination are the tessellations that are semi-regular and that are formed from what is the set of eight semi-regular tessellations and three three-sectioned regular cuts. Thus, a total of fourteen demirregular tessellations are shaped.

exist examples of tessellations around the world. It is known as tessellated from Cairo to the tessellation composed of a pentagon with four sides of identical measure and a sum of the angles of 540º (two of 108º, two of 90º and one of 144º).

Another popular type of tessellation is the penrose tessellation , whose name honors the British mathematician Roger Penrose . These tessellations are aperiodic (they do not have translational symmetry): two have rotational symmetry of order five and axis of symmetry.

Many are the artists who, throughout their career, have opted for tessellation as a key piece for the development of their works. However, among the most significant is the Dutchman Maurits Cornelis Escher, artistically known as M. C. Escher. This became a reference at the time because he resorted to tessellation to combine it with the plane and create all kinds of forms, such as animals of various kinds, among which are fish and birds.

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